How to play
The rules
Fill the 9×9 grid so that every row, every column and each of the nine 3×3 boxes contains the digits 1 to 9 exactly once. The digits printed in bold at the start are clues — they cannot be changed. Every puzzle here has exactly one solution, and every one can be reached by reasoning. You never need to guess.
Getting around
- Tap or click a cell to select it, then use the number pad or your keyboard.
- Arrow keys move the selection, 1–9 place a digit, 0 or Backspace clears one, and Ctrl/⌘ + Z undoes.
- Notes mode writes small pencil marks instead of a digit — hold Shift with a number to add one without switching modes. Pencil marks are how every technique past the first one is actually spotted.
- A digit that clashes with another in its row, column or box turns red. Wrong entries are allowed on purpose: noticing and fixing them is part of solving.
Explain next step
This is what makes this site different from a puzzle grid. Press it and the board is analysed as it stands right now: the cells that justify the next move are spotlighted, the row, column or box the reasoning happens in is outlined, and a card spells the argument out in a sentence.
Apply makes the move for you — as an ordinary move you can undo. Got it dismisses the card and leaves the board alone, which is the button to use if you would rather make the move yourself.
If none of the four techniques below applies, it says so plainly instead of inventing an explanation. On Expert puzzles that will happen, because Expert is defined as needing patterns beyond these four.
The four techniques
They are listed easiest first, and that is the order they are checked in — you always get the simplest explanation that fits the board.
1. Naked single
A cell with only one candidate left.
Pick an empty cell and list the digits missing from its row, its column and its box. If exactly one digit survives all three, it goes there.
Example. A row already holds 1 through 8. The last empty cell in it can only be 9 — nothing else is left to put there.
2. Hidden single
A digit with only one place left in a row, column or box.
Take one digit at a time and cross out every cell in a unit that cannot hold it, because the digit already appears in that cell’s row, column or box. If one cell survives, the digit belongs there.
Example. A box has five empty cells, but four of them already see a 5 elsewhere in their row or column. The fifth cell must be the 5 — the box has to contain one somewhere.
3. Naked pair
Two cells in one unit that share the same two candidates.
If two cells in a unit both come down to exactly {a, b}, then between them they use up both digits. Neither can appear anywhere else in that unit, so remove both from every other cell there.
Example. Two cells in a box can only be 3 or 7. You do not know which is which — but you know no other cell in that box can be 3 or 7.
4. Pointing pair
A digit confined to two cells of a box that share a row or column.
If a digit can only go in two cells of a box and both sit in the same line, then the box’s copy of that digit is somewhere on that line. Remove the digit from the rest of the line outside the box.
Example. In the top-left box, 7 can only go in two cells, both in row 1. Wherever it lands, row 1 gets its 7 from that box — so no other cell in row 1 can hold a 7.
How the difficulties are set
By what you have to know, not by how many clues are on the board. Clue count is a poor guide — a 30-clue puzzle can be gentle and a 32-clue one brutal. Each puzzle is solved by a program that only knows the techniques above, and graded by which ones it needed:
- Easy — naked singles alone are enough.
- Medium — hidden singles are also needed.
- Hard — naked pairs or pointing pairs are also needed.
- Expert — the four techniques are not enough. Still solvable, still exactly one answer, but it will take patterns this app does not yet teach.
Why clue count is a poor measure of difficulty goes into this properly, including the proven 17-clue minimum.
The guides
The page above is the reference; these are the explanations. Each one works through a technique on a real position, with diagrams — including the patterns this app does not yet teach, which is what Expert puzzles need.
- How to solve Sudoku: a beginner’s guideLearn Sudoku from scratch: the one rule that matters, how to scan a grid, the first two techniques that solve most easy puzzles, and what to do when you get stuck.
- Naked singles and hidden singles explainedThe two techniques that finish most Sudoku puzzles, and the difference between them. Worked grids for each, plus why hidden singles are so much harder to spot.
- Sudoku pencil marks: how to use notation properlyWhen to start marking candidates, how much to write down, and how to keep marks from going stale. The habit that separates people who finish hard puzzles from those who stall.
- Naked pairs, triples and quads in SudokuHow locked sets work: two cells sharing two candidates, three sharing three, and why the counting argument behind them is the same every time. With verified grids.
- Hidden pairs and hidden triples in SudokuHidden subsets are the mirror image of naked ones, and often easier to spot once you know to count digits instead of comparing cells. Worked example on a real grid.
- Pointing pairs and box/line reductionLocked candidates in both directions: when a digit in a box is stuck on one line, and when a digit on a line is stuck in one box. Both shown on the same grid.
- The X-wing technique in Sudoku, explainedThe first advanced Sudoku pattern worth learning: what an X-wing is, the argument that makes it work, how to find one, and when it is a waste of time to look.
- How to solve Sudoku fasterSpeed in Sudoku comes from search order, not from thinking quicker. A concrete scanning routine, what to do when stuck, and the habits that waste the most time.
- Nine common Sudoku mistakes, and how to stop making themGuessing, stale pencil marks, checking only one line, restarting instead of debugging. The specific errors that cost solvers the most time, and the fix for each.
- What actually makes a Sudoku puzzle hard?Clue count is a bad measure of difficulty, and here is why. How puzzles are really graded, why 17 clues is the minimum, and what “unique solution” guarantees.